pacman::p_load(tmap, sf, DT, stplanr, sp, dplyr,
performance, reshape2, units,
ggpubr, tidyverse, mapview, httr, sfheaders, knitr, kableExtra)take home exercise 2 Singapore public bus commuter flows
overview
We currently have data on people’s movement patterns as well as information on schools, businesses, and retail activities in different areas. The goal of this task is to identify common Saturday activities among the population. Through our analysis, we aim to provide recommendations to the government, suggesting potential enhancements to existing facilities or proposing the development of new amenities that align with people’s preferences. The objective is to make these facilities more appealing and strategically located for the community’s convenience.
Objective
Our goal is to pinpoint popular weekend destinations, analyze the main facilities in those areas, and provide recommendations accordingly.
Data Geospatial data:
Passenger Volume by Origin Destination Bus Stops, Bus Stop Location, Train Station and Train Station Exit Point, Master Plan 2019 Subzone Boundary, HDB Property Information, Business, Entertn, F&B, FinServ, Leisure&Recreation and Retails. Aspatial data: HDB Property Information. This data is for us to use.
Mmethodology ：
1，Prepare hexagonal data. 2，Draw the flow data map for Saturday morning. 3，Prepare the destination data for customer activities on Saturday. 4，Data integration. 5，Model. 6，Visualization. 7, Limitation
1，Prepare hexagonal data.
Importing the OD data
odbus <- read_csv("data/aspatial/origin_destination_bus_202310.csv")Rows: 5694297 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (5): YEAR_MONTH, DAY_TYPE, PT_TYPE, ORIGIN_PT_CODE, DESTINATION_PT_CODE
dbl (2): TIME_PER_HOUR, TOTAL_TRIPS
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) glimpse(odbus)Rows: 5,694,297
Columns: 7
$ YEAR_MONTH <chr> "2023-10", "2023-10", "2023-10", "2023-10", "2023-…
$ DAY_TYPE <chr> "WEEKENDS/HOLIDAY", "WEEKDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR <dbl> 16, 16, 14, 14, 17, 17, 17, 7, 14, 14, 10, 20, 20,…
$ PT_TYPE <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE <fct> 04168, 04168, 80119, 80119, 44069, 20281, 20281, 1…
$ DESTINATION_PT_CODE <fct> 10051, 10051, 90079, 90079, 17229, 20141, 20141, 1…
$ TOTAL_TRIPS <dbl> 3, 5, 3, 5, 4, 1, 24, 2, 1, 7, 3, 2, 5, 1, 1, 1, 1…weekendmorning11_14 <- odbus %>%
filter(DAY_TYPE == "WEEKENDS/HOLIDAY") %>%
filter(TIME_PER_HOUR >= 11 & TIME_PER_HOUR <= 14) %>%
group_by(ORIGIN_PT_CODE, DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS), .groups = 'keep')datatable(weekendmorning11_14)Warning in instance$preRenderHook(instance): It seems your data is too big for
client-side DataTables. You may consider server-side processing:
https://rstudio.github.io/DT/server.htmlwrite_rds(weekendmorning11_14, "data/rds/weekendmorning11_14.rds")weekendmorning11_14 <- read_rds("data/rds/weekendmorning11_14.rds")busstop points
busstop <- st_read(dsn = "data/geospatial", layer = "BusStop") %>%
st_transform(crs = 3414)Reading layer `BusStop' from data source
`/Users/linxu/ISSS624/take home exercise 2/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21glimpse(busstop)Rows: 5,161
Columns: 4
$ BUS_STOP_N <chr> "22069", "32071", "44331", "96081", "11561", "66191", "2338…
$ BUS_ROOF_N <chr> "B06", "B23", "B01", "B05", "B05", "B03", "B02A", "B02", "B…
$ LOC_DESC <chr> "OPP CEVA LOGISTICS", "AFT TRACK 13", "BLK 239", "GRACE IND…
$ geometry <POINT [m]> POINT (13576.31 32883.65), POINT (13228.59 44206.38),…busstop_points = busstop %>%
st_as_sf(coords = c("geometry"), crs = 3414, remove = FALSE)mapview_busstop_points = mapview(busstop_points, cex = 0.5, alpha = .5, popup = NULL)
mapview_busstop_pointsarea_honeycomb_grid = st_make_grid(busstop_points, c(750, 750), what = "polygons", square = FALSE)
honeycomb_grid_sf = st_sf(area_honeycomb_grid) %>%
mutate(grid_id = 1:length(lengths(area_honeycomb_grid)))
honeycomb_grid_sf$n_colli = lengths(st_intersects(honeycomb_grid_sf, busstop_points))
honeycomb_count = filter(honeycomb_grid_sf, n_colli > 0)write_rds(honeycomb_count, "data/rds/honeycomb_count.rds")map_honeycomb = tm_shape(honeycomb_count) +
tm_fill(
col = "n_colli",
palette = "Reds",
style = "cont",
title = "Number of collisions",
id = "grid_id",
showNA = FALSE,
alpha = 0.6,
popup.vars = c(
"Number of collisions: " = "n_colli"
),
popup.format = list(
n_colli = list(format = "f", digits = 0)
)
) +
tm_borders(col = "grey40", lwd = 0.7)
map_honeycomb
busstop_honeycomb_count <- st_intersection(busstop, honeycomb_count) %>%
select(BUS_STOP_N, grid_id) %>%
st_drop_geometry()Warning: attribute variables are assumed to be spatially constant throughout
all geometriesglimpse(busstop_honeycomb_count)Rows: 5,161
Columns: 2
$ BUS_STOP_N <chr> "25059", "25751", "26379", "26369", "25741", "26399", "2571…
$ grid_id <int> 23, 44, 46, 46, 66, 67, 67, 67, 67, 68, 86, 87, 88, 88, 88,…write_rds(busstop_honeycomb_count, "data/rds/busstop_honeycomb_count.rds") 2,Draw the flow data map for Saturday morning.
weekendmorning11_14 <- left_join(weekendmorning11_14 , busstop_honeycomb_count,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_SZ = grid_id,
DESTIN_BS = DESTINATION_PT_CODE)Warning in left_join(weekendmorning11_14, busstop_honeycomb_count, by = c(ORIGIN_PT_CODE = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 27736 of `x` matches multiple rows in `y`.
ℹ Row 3057 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
"many-to-many"` to silence this warning.duplicate <- weekendmorning11_14 %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekendmorning11_14 <- unique(weekendmorning11_14)weekendmorning11_14 <- left_join(weekendmorning11_14 , busstop_honeycomb_count,
by = c("DESTIN_BS" = "BUS_STOP_N")) Warning in left_join(weekendmorning11_14, busstop_honeycomb_count, by = c(DESTIN_BS = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 206 of `x` matches multiple rows in `y`.
ℹ Row 3146 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
"many-to-many"` to silence this warning.duplicate <- weekendmorning11_14 %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekendmorning11_14 <- unique(weekendmorning11_14)weekendmorning11_14 <- weekendmorning11_14 %>%
rename(DESTIN_SZ = grid_id) %>%
drop_na() %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarise(WEEKENDDAYMORNING_PEAK = sum(TRIPS))`summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.write_rds(weekendmorning11_14, "data/rds/weekendmorning11_14.rds")weekendmorning11_14 <- read_rds("data/rds/weekendmorning11_14.rds")weekendmorning11_14_1 <- weekendmorning11_14[weekendmorning11_14$ORIGIN_SZ!=weekendmorning11_14$DESTIN_SZ,]flowLine <- od2line(flow = weekendmorning11_14_1,
zones = honeycomb_count,
zone_code = "grid_id")Creating centroids representing desire line start and end points.tm_shape(honeycomb_count) +
tm_polygons() +
flowLine %>%
tm_shape() +
tm_lines(lwd = "WEEKENDDAYMORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.3)Warning in g$scale * (w_legend/maxW): longer object length is not a multiple of
shorter object lengthWarning in g$scale * (x/maxW): longer object length is not a multiple of
shorter object length
tm_shape(honeycomb_count) +
tm_polygons() +
flowLine %>%
filter(WEEKENDDAYMORNING_PEAK >= 2000) %>%
tm_shape() +
tm_lines(lwd = "WEEKENDDAYMORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.3)Warning in g$scale * (w_legend/maxW): longer object length is not a multiple of
shorter object length
Caculate the distance
honeycomb_count <- read_rds("data/rds/honeycomb_count.rds")
honeycomb_countSimple feature collection with 834 features and 2 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 3595.122 ymin: 26049.09 xmax: 48595.12 ymax: 53545.39
Projected CRS: SVY21 / Singapore TM
First 10 features:
area_honeycomb_grid grid_id n_colli
1 POLYGON ((3970.122 27348.13... 23 1
2 POLYGON ((4345.122 27997.65... 44 1
3 POLYGON ((4345.122 30595.72... 46 2
4 POLYGON ((4720.122 28647.16... 66 1
5 POLYGON ((4720.122 29946.2,... 67 4
6 POLYGON ((4720.122 31245.24... 68 1
7 POLYGON ((5095.122 27997.65... 86 1
8 POLYGON ((5095.122 29296.68... 87 1
9 POLYGON ((5095.122 30595.72... 88 4
10 POLYGON ((5095.122 31894.76... 89 2honeycomb_count_sp <- as(honeycomb_count, "Spatial")
honeycomb_count_spclass : SpatialPolygonsDataFrame
features : 834
extent : 3595.122, 48595.12, 26049.09, 53545.39 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 2
names : grid_id, n_colli
min values : 23, 1
max values : 2505, 19 dist <- spDists(honeycomb_count_sp,
longlat = FALSE)
head(dist, n=c(10, 10)) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0.000 750.000 3269.174 1500.000 2704.163 3968.627 1299.038 2250.000
[2,] 750.000 0.000 2598.076 750.000 1984.313 3269.174 750.000 1500.000
[3,] 3269.174 2598.076 0.000 1984.313 750.000 750.000 2704.163 1500.000
[4,] 1500.000 750.000 1984.313 0.000 1299.038 2598.076 750.000 750.000
[5,] 2704.163 1984.313 750.000 1299.038 0.000 1299.038 1984.313 750.000
[6,] 3968.627 3269.174 750.000 2598.076 1299.038 0.000 3269.174 1984.313
[7,] 1299.038 750.000 2704.163 750.000 1984.313 3269.174 0.000 1299.038
[8,] 2250.000 1500.000 1500.000 750.000 750.000 1984.313 1299.038 0.000
[9,] 3436.932 2704.163 750.000 1984.313 750.000 750.000 2598.076 1299.038
[10,] 4683.748 3968.627 1500.000 3269.174 1984.313 750.000 3897.114 2598.076
[,9] [,10]
[1,] 3436.932 4683.748
[2,] 2704.163 3968.627
[3,] 750.000 1500.000
[4,] 1984.313 3269.174
[5,] 750.000 1984.313
[6,] 750.000 750.000
[7,] 2598.076 3897.114
[8,] 1299.038 2598.076
[9,] 0.000 1299.038
[10,] 1299.038 0.000sz_names <- honeycomb_count$grid_idcolnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)distPair <- melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 23 23 0.000
2 44 23 750.000
3 46 23 3269.174
4 66 23 1500.000
5 67 23 2704.163
6 68 23 3968.627
7 86 23 1299.038
8 87 23 2250.000
9 88 23 3436.932
10 89 23 4683.748distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
Min. : 23 Min. : 23 Min. : 750
1st Qu.: 871 1st Qu.: 871 1st Qu.: 8352
Median :1324 Median :1324 Median :13332
Mean :1269 Mean :1269 Mean :14162
3rd Qu.:1688 3rd Qu.:1688 3rd Qu.:18929
Max. :2505 Max. :2505 Max. :44680 distPair$dist <- ifelse(distPair$dist == 0,
50, distPair$dist)distPair %>%
summary() Var1 Var2 dist
Min. : 23 Min. : 23 Min. : 50
1st Qu.: 871 1st Qu.: 871 1st Qu.: 8250
Median :1324 Median :1324 Median :13332
Mean :1269 Mean :1269 Mean :14145
3rd Qu.:1688 3rd Qu.:1688 3rd Qu.:18929
Max. :2505 Max. :2505 Max. :44680 distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)write_rds(distPair, "data/rds/distPair.rds") weekendmorning11_14 <- read_rds("data/rds/weekendmorning11_14.rds")flow_data <- weekendmorning11_14 %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarize(TRIPS = sum(WEEKENDDAYMORNING_PEAK)) `summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.head(flow_data)# A tibble: 6 × 3
# Groups: ORIGIN_SZ [2]
ORIGIN_SZ DESTIN_SZ TRIPS
<int> <int> <dbl>
1 44 128 4
2 44 129 2
3 44 175 20
4 46 67 2
5 46 111 6
6 46 134 73flow_data$FlowNoIntra <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0, flow_data$TRIPS)
flow_data$offset <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0.000001, 1)flow_data$ORIGIN_SZ <- as.integer(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.integer(flow_data$DESTIN_SZ)
distPair$orig <- as.integer(distPair$orig)
distPair$dest <- as.integer(distPair$dest)
distPair$dist <- as.integer(distPair$dist)flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "orig",
"DESTIN_SZ" = "dest"))glimpse(flow_data1)Rows: 62,398
Columns: 6
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ <int> 44, 44, 44, 46, 46, 46, 46, 46, 66, 66, 66, 67, 67, 67, 67…
$ DESTIN_SZ <int> 128, 129, 175, 67, 111, 134, 155, 406, 44, 134, 175, 44, 8…
$ TRIPS <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25, 28, 1, …
$ FlowNoIntra <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25, 28, 1, …
$ offset <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ dist <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750, 7232, …flow_data1 <- flow_data1 %>%
left_join(honeycomb_count,
by = c("DESTIN_SZ" = "grid_id")) %>%
rename(DIST = dist)summary(flow_data1) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Min. : 44 Min. : 44 Min. : 1.0 Min. : 0.0
1st Qu.:1119 1st Qu.:1119 1st Qu.: 4.0 1st Qu.: 4.0
Median :1435 Median :1435 Median : 14.0 Median : 14.0
Mean :1423 Mean :1423 Mean : 120.5 Mean : 115.7
3rd Qu.:1727 3rd Qu.:1727 3rd Qu.: 58.0 3rd Qu.: 56.0
Max. :2505 Max. :2505 Max. :43418.0 Max. :43418.0
offset DIST area_honeycomb_grid n_colli
Min. :0.000001 Min. : 50 POLYGON :62398 Min. : 1.000
1st Qu.:1.000000 1st Qu.: 2704 epsg:3414 : 0 1st Qu.: 5.000
Median :1.000000 Median : 5250 +proj=tmer...: 0 Median : 8.000
Mean :0.990865 Mean : 6224 Mean : 7.929
3rd Qu.:1.000000 3rd Qu.: 8649 3rd Qu.:10.000
Max. :1.000000 Max. :24784 Max. :19.000 write_rds(flow_data1,
"data/rds/flow_data1.rds")#3，Prepare the destination data for customer activities on Saturday.
Schools
url<-"https://www.onemap.gov.sg/api/common/elastic/search"
csv<-read_csv("data/aspatial/Generalinformationofschools.csv")Rows: 346 Columns: 31
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (31): school_name, url_address, address, postal_code, telephone_no, tele...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.postcodes<-csv$`postal_code`
found<-data.frame()
not_found<-data.frame()
for(postcode in postcodes){
query<-list('searchVal'=postcode,'returnGeom'='Y','getAddrDetails'='Y','pageNum'='1')
res<- GET(url,query=query)
if((content(res)$found)!=0){
found<-rbind(found,data.frame(content(res))[4:13])
} else{
not_found = data.frame(postcode)
}
}merged = merge(csv, found, by.x = 'postal_code', by.y = 'results.POSTAL', all = TRUE)
write.csv(merged, file = "data/aspatial/schools.csv")
write.csv(not_found, file = "data/aspatial/not_found.csv")schools <- read_csv("data/aspatial/schools.csv") %>%
rename(latitude = "results.LATITUDE",
longitude = "results.LONGITUDE")%>%
select(postal_code, school_name, latitude, longitude)New names:
Rows: 350 Columns: 41
── Column specification
──────────────────────────────────────────────────────── Delimiter: "," chr
(36): postal_code, school_name, url_address, address, telephone_no, tele... dbl
(5): ...1, results.X, results.Y, results.LATITUDE, results.LONGITUDE
ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
Specify the column types or set `show_col_types = FALSE` to quiet this message.
• `` -> `...1`schools <- schools[complete.cases(schools$longitude, schools$latitude), ]
schools_sf <- st_as_sf(schools,
coords = c("longitude", "latitude"),
crs=4326) %>%
st_transform(crs = 3414)tmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
tm_polygons() +
tm_shape(schools_sf) +
tm_dots()
tmap_mode("plot")tmap mode set to plottinghoneycomb_count$`SCHOOL_COUNT`<- lengths(
st_intersects(
honeycomb_count, schools_sf))summary(honeycomb_count$SCHOOL_COUNT) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.0000 0.0000 0.4113 1.0000 4.0000 RapidTransitSystemStation
RTSS_sf <- st_read(dsn = "data/geospatial/",
layer = "RapidTransitSystemStation")%>%
st_transform(crs = 3414)Reading layer `RapidTransitSystemStation' from data source
`/Users/linxu/ISSS624/take home exercise 2/data/geospatial'
using driver `ESRI Shapefile'Warning in CPL_read_ogr(dsn, layer, query, as.character(options), quiet, : GDAL
Message 1: Non closed ring detected. To avoid accepting it, set the
OGR_GEOMETRY_ACCEPT_UNCLOSED_RING configuration option to NOSimple feature collection with 220 features and 4 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 6068.209 ymin: 27478.44 xmax: 45377.5 ymax: 47913.58
Projected CRS: SVY21RTSS_sf_polygons <- RTSS_sf[st_is_valid(RTSS_sf), ]
RTSS_sf_points <- st_centroid(RTSS_sf_polygons)Warning: st_centroid assumes attributes are constant over geometriestmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
tm_polygons() +
tm_shape(RTSS_sf_points) +
tm_dots()Warning: The shape RTSS_sf_points contains empty units.
tmap_mode("plot")tmap mode set to plottinghoneycomb_count$`RTSS_COUNT`<- lengths(
st_intersects(
honeycomb_count, RTSS_sf_points))summary(honeycomb_count$`RTSS_COUNT`) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.0000 0.0000 0.2542 0.0000 4.0000 Entertn
entertn_sf <- st_read(dsn = "data/geospatial/",
layer = "entertn")%>%
st_transform(crs = 3414)Reading layer `entertn' from data source
`/Users/linxu/ISSS624/take home exercise 2/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 114 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 10809.34 ymin: 26528.63 xmax: 41600.62 ymax: 46375.77
Projected CRS: SVY21 / Singapore TMtmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
tm_polygons() +
tm_shape(entertn_sf) +
tm_dots()
tmap_mode("plot")tmap mode set to plottinghoneycomb_count$`ENTERTN_COUNT`<- lengths(
st_intersects(
honeycomb_count, entertn_sf))summary(honeycomb_count$ENTERTN_COUNT) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.0000 0.0000 0.1331 0.0000 9.0000 Liesure&Recreation
lr_sf <- st_read(dsn = "data/geospatial/",
layer = "Liesure&Recreation") %>%
st_transform(crs = 3414)Reading layer `Liesure&Recreation' from data source
`/Users/linxu/ISSS624/take home exercise 2/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 1217 features and 30 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6010.495 ymin: 25134.28 xmax: 48439.77 ymax: 50078.88
Projected CRS: SVY21 / Singapore TMtmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
tm_polygons() +
tm_shape(lr_sf) +
tm_dots()
tmap_mode("plot")tmap mode set to plottinghoneycomb_count$`LR_COUNT`<- lengths(
st_intersects(
honeycomb_count, lr_sf))summary(honeycomb_count$LR_COUNT) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 0.000 0.000 1.307 1.000 41.000 Retails
retails_sf <- st_read(dsn = "data/geospatial/",
layer = "Retails")%>%
st_transform(crs = 3414)Reading layer `Retails' from data source
`/Users/linxu/ISSS624/take home exercise 2/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 37635 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 4737.982 ymin: 25171.88 xmax: 48265.04 ymax: 50135.28
Projected CRS: SVY21 / Singapore TMtmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
tm_polygons() +
tm_shape(retails_sf) +
tm_dots()
tmap_mode("plot")tmap mode set to plottinghoneycomb_count$`RETAILS_COUNT`<- lengths(
st_intersects(
honeycomb_count, retails_sf))glimpse(honeycomb_count$RETAILS_COUNT) int [1:834] 0 0 0 0 5 0 0 0 5 1 ...4,Data integration.
honeycomb_count_tidy <- honeycomb_count %>%
st_drop_geometry() %>%
select(grid_id, SCHOOL_COUNT, RTSS_COUNT, ENTERTN_COUNT, LR_COUNT, RETAILS_COUNT)flow_data2 <- flow_data1 %>%
left_join(honeycomb_count_tidy,
by = c("DESTIN_SZ" = "grid_id")) glimpse(flow_data2)Rows: 62,398
Columns: 13
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ <int> 44, 44, 44, 46, 46, 46, 46, 46, 66, 66, 66, 67, 67…
$ DESTIN_SZ <int> 128, 129, 175, 67, 111, 134, 155, 406, 44, 134, 17…
$ TRIPS <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ FlowNoIntra <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ offset <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DIST <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750…
$ area_honeycomb_grid <POLYGON [m]> POLYGON ((5845.122 27997.65..., POLYGON ((…
$ n_colli <int> 1, 1, 11, 4, 5, 1, 5, 9, 1, 1, 11, 1, 4, 2, 5, 1, …
$ SCHOOL_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ RTSS_COUNT <int> 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,…
$ ENTERTN_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ LR_COUNT <int> 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,…
$ RETAILS_COUNT <int> 0, 0, 2, 5, 4, 3, 0, 16, 0, 3, 2, 0, 5, 1, 4, 0, 3…flow_data2$SCHOOL_COUNT <- ifelse(
flow_data2$SCHOOL_COUNT == 0,
0.99, flow_data2$SCHOOL_COUNT)
flow_data2$RTSS_COUNT <- ifelse(
flow_data2$RTSS_COUNT == 0,
0.99, flow_data2$RTSS_COUNT)
flow_data2$ENTERTN_COUNT <- ifelse(
flow_data2$ENTERTN_COUNT == 0,
0.99, flow_data2$ENTERTN_COUNT)
flow_data2$LR_COUNT <- ifelse(
flow_data2$LR_COUNT == 0,
0.99, flow_data2$LR_COUNT)
flow_data2$RETAILS_COUNT <- ifelse(
flow_data2$RETAILS_COUNT == 0,
0.99, flow_data2$RETAILS_COUNT)summary(flow_data2) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Min. : 44 Min. : 44 Min. : 1.0 Min. : 0.0
1st Qu.:1119 1st Qu.:1119 1st Qu.: 4.0 1st Qu.: 4.0
Median :1435 Median :1435 Median : 14.0 Median : 14.0
Mean :1423 Mean :1423 Mean : 120.5 Mean : 115.7
3rd Qu.:1727 3rd Qu.:1727 3rd Qu.: 58.0 3rd Qu.: 56.0
Max. :2505 Max. :2505 Max. :43418.0 Max. :43418.0
offset DIST area_honeycomb_grid n_colli
Min. :0.000001 Min. : 50 POLYGON :62398 Min. : 1.000
1st Qu.:1.000000 1st Qu.: 2704 epsg:3414 : 0 1st Qu.: 5.000
Median :1.000000 Median : 5250 +proj=tmer...: 0 Median : 8.000
Mean :0.990865 Mean : 6224 Mean : 7.929
3rd Qu.:1.000000 3rd Qu.: 8649 3rd Qu.:10.000
Max. :1.000000 Max. :24784 Max. :19.000
SCHOOL_COUNT RTSS_COUNT ENTERTN_COUNT LR_COUNT
Min. :0.990 Min. :0.990 Min. :0.990 Min. : 0.990
1st Qu.:0.990 1st Qu.:0.990 1st Qu.:0.990 1st Qu.: 0.990
Median :0.990 Median :0.990 Median :0.990 Median : 1.000
Mean :1.178 Mean :1.125 Mean :1.183 Mean : 2.703
3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:0.990 3rd Qu.: 3.000
Max. :4.000 Max. :4.000 Max. :9.000 Max. :41.000
RETAILS_COUNT
Min. : 0.99
1st Qu.: 7.00
Median : 30.00
Mean : 96.65
3rd Qu.: 107.00
Max. :1678.00 write_rds(flow_data2,
"data/rds/flow_data_tidy.rds")flow_data3 <- read_rds("data/rds/flow_data_tidy.rds")flow_data3 <- flow_data2 %>%
mutate(ORIGIN_SZ = as.character(ORIGIN_SZ), DESTIN_SZ = as.character(DESTIN_SZ))glimpse(flow_data3)Rows: 62,398
Columns: 13
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ <chr> "44", "44", "44", "46", "46", "46", "46", "46", "6…
$ DESTIN_SZ <chr> "128", "129", "175", "67", "111", "134", "155", "4…
$ TRIPS <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ FlowNoIntra <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ offset <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DIST <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750…
$ area_honeycomb_grid <POLYGON [m]> POLYGON ((5845.122 27997.65..., POLYGON ((…
$ n_colli <int> 1, 1, 11, 4, 5, 1, 5, 9, 1, 1, 11, 1, 4, 2, 5, 1, …
$ SCHOOL_COUNT <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ RTSS_COUNT <dbl> 0.99, 0.99, 1.00, 0.99, 0.99, 0.99, 1.00, 1.00, 0.…
$ ENTERTN_COUNT <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ LR_COUNT <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 1.00, 0.99, 0.99, 0.…
$ RETAILS_COUNT <dbl> 0.99, 0.99, 2.00, 5.00, 4.00, 3.00, 0.99, 16.00, 0…kable(head(flow_data3[, 1:5], n = 5))| ORIGIN_SZ | DESTIN_SZ | TRIPS | FlowNoIntra | offset |
|---|---|---|---|---|
| 44 | 128 | 4 | 4 | 1 |
| 44 | 129 | 2 | 2 | 1 |
| 44 | 175 | 20 | 20 | 1 |
| 46 | 67 | 2 | 2 | 1 |
| 46 | 111 | 6 | 6 | 1 |
flow_data3$FlowNoIntra <- ifelse(
flow_data3$ORIGIN_SZ == flow_data3$DESTIN_SZ,
0, flow_data3$TRIPS)
flow_data3$offset <- ifelse(
flow_data3$ORIGIN_SZ == flow_data3$DESTIN_SZ,
0.000001, 1)inter_zonal_flow <- flow_data3 %>%
filter(FlowNoIntra > 0)glimpse(inter_zonal_flow)Rows: 61,828
Columns: 13
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ <chr> "44", "44", "44", "46", "46", "46", "46", "46", "6…
$ DESTIN_SZ <chr> "128", "129", "175", "67", "111", "134", "155", "4…
$ TRIPS <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ FlowNoIntra <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ offset <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DIST <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750…
$ area_honeycomb_grid <POLYGON [m]> POLYGON ((5845.122 27997.65..., POLYGON ((…
$ n_colli <int> 1, 1, 11, 4, 5, 1, 5, 9, 1, 1, 11, 1, 4, 2, 5, 1, …
$ SCHOOL_COUNT <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ RTSS_COUNT <dbl> 0.99, 0.99, 1.00, 0.99, 0.99, 0.99, 1.00, 1.00, 0.…
$ ENTERTN_COUNT <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ LR_COUNT <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 1.00, 0.99, 0.99, 0.…
$ RETAILS_COUNT <dbl> 0.99, 0.99, 2.00, 5.00, 4.00, 3.00, 0.99, 16.00, 0…5,Model
Origin_Constrained model
orcSIM_Poisson <- glm(formula = TRIPS ~
ORIGIN_SZ +
log(SCHOOL_COUNT) +
log(ENTERTN_COUNT) +
log(RTSS_COUNT) +
log(LR_COUNT) +
log(RETAILS_COUNT) +
log(DIST) - 1,
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)
summary(orcSIM_Poisson)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(SCHOOL_COUNT) + log(ENTERTN_COUNT) +
log(RTSS_COUNT) + log(LR_COUNT) + log(RETAILS_COUNT) + log(DIST) -
1, family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
ORIGIN_SZ1001 13.9522257 0.0481911 289.52 <2e-16 ***
ORIGIN_SZ1003 16.5614723 0.0074577 2220.74 <2e-16 ***
ORIGIN_SZ1004 16.8635747 0.0072645 2321.38 <2e-16 ***
ORIGIN_SZ1011 13.8901017 0.0368240 377.20 <2e-16 ***
ORIGIN_SZ1012 14.7621749 0.0239745 615.75 <2e-16 ***
ORIGIN_SZ1013 14.4064067 0.0199029 723.83 <2e-16 ***
ORIGIN_SZ1014 14.3918837 0.0184347 780.70 <2e-16 ***
ORIGIN_SZ1015 13.7171479 0.0263921 519.75 <2e-16 ***
ORIGIN_SZ1016 15.7463647 0.0093067 1691.94 <2e-16 ***
ORIGIN_SZ1018 15.2690538 0.0201405 758.13 <2e-16 ***
ORIGIN_SZ1019 16.9424129 0.0082493 2053.79 <2e-16 ***
ORIGIN_SZ1023 15.1842163 0.0191954 791.03 <2e-16 ***
ORIGIN_SZ1024 16.3446959 0.0091104 1794.08 <2e-16 ***
ORIGIN_SZ1025 13.4718382 0.0536448 251.13 <2e-16 ***
ORIGIN_SZ1033 14.6499350 0.0173378 844.97 <2e-16 ***
ORIGIN_SZ1034 15.2168146 0.0122121 1246.04 <2e-16 ***
ORIGIN_SZ1035 15.3979009 0.0109772 1402.72 <2e-16 ***
ORIGIN_SZ1036 15.4696030 0.0110899 1394.92 <2e-16 ***
ORIGIN_SZ1037 15.3548825 0.0103197 1487.93 <2e-16 ***
ORIGIN_SZ1043 15.5737689 0.0206645 753.65 <2e-16 ***
ORIGIN_SZ1045 16.3356712 0.0080020 2041.44 <2e-16 ***
ORIGIN_SZ1046 16.2164649 0.0096998 1671.84 <2e-16 ***
ORIGIN_SZ1053 14.9450437 0.0135442 1103.43 <2e-16 ***
ORIGIN_SZ1054 14.3737794 0.0180907 794.54 <2e-16 ***
ORIGIN_SZ1055 15.6201549 0.0098605 1584.11 <2e-16 ***
ORIGIN_SZ1056 14.7422819 0.0155813 946.15 <2e-16 ***
ORIGIN_SZ1064 13.1960411 0.1796497 73.45 <2e-16 ***
ORIGIN_SZ1066 16.4904787 0.0075434 2186.09 <2e-16 ***
ORIGIN_SZ1067 15.0011162 0.0215949 694.66 <2e-16 ***
ORIGIN_SZ1074 14.9653575 0.0141761 1055.67 <2e-16 ***
ORIGIN_SZ1075 13.1867670 0.0353658 372.87 <2e-16 ***
ORIGIN_SZ1076 14.5056392 0.0152828 949.15 <2e-16 ***
ORIGIN_SZ1077 14.4224563 0.0189463 761.23 <2e-16 ***
ORIGIN_SZ1079 15.3679551 0.0110576 1389.81 <2e-16 ***
ORIGIN_SZ1085 13.0115857 0.1043134 124.74 <2e-16 ***
ORIGIN_SZ1087 15.6005199 0.0121817 1280.65 <2e-16 ***
ORIGIN_SZ1088 14.3097821 0.0233528 612.77 <2e-16 ***
ORIGIN_SZ109 14.7306481 0.1032158 142.72 <2e-16 ***
ORIGIN_SZ1094 12.9356281 0.0825621 156.68 <2e-16 ***
ORIGIN_SZ1095 13.2564397 0.0535590 247.51 <2e-16 ***
ORIGIN_SZ1096 13.4953340 0.0510736 264.23 <2e-16 ***
ORIGIN_SZ1097 16.0412821 0.0074435 2155.06 <2e-16 ***
ORIGIN_SZ1098 13.6072833 0.0317402 428.71 <2e-16 ***
ORIGIN_SZ1099 15.1281740 0.0120480 1255.66 <2e-16 ***
ORIGIN_SZ110 15.1219984 0.0774656 195.21 <2e-16 ***
ORIGIN_SZ1105 16.1984686 0.0194475 832.93 <2e-16 ***
ORIGIN_SZ1106 12.2541101 0.1474864 83.09 <2e-16 ***
ORIGIN_SZ1107 14.2678299 0.0382472 373.04 <2e-16 ***
ORIGIN_SZ1108 17.7342041 0.0048102 3686.75 <2e-16 ***
ORIGIN_SZ1109 15.1083437 0.0216983 696.29 <2e-16 ***
ORIGIN_SZ111 17.0334941 0.0144287 1180.53 <2e-16 ***
ORIGIN_SZ1116 14.1947917 0.0199302 712.23 <2e-16 ***
ORIGIN_SZ1117 13.9156612 0.0238805 582.72 <2e-16 ***
ORIGIN_SZ1118 13.2485570 0.0359039 369.00 <2e-16 ***
ORIGIN_SZ1119 14.7977994 0.0137204 1078.53 <2e-16 ***
ORIGIN_SZ112 13.0830540 0.1644403 79.56 <2e-16 ***
ORIGIN_SZ1120 14.1557789 0.0235980 599.87 <2e-16 ***
ORIGIN_SZ1129 16.2752021 0.0095842 1698.12 <2e-16 ***
ORIGIN_SZ1130 16.2138007 0.0085591 1894.34 <2e-16 ***
ORIGIN_SZ1131 15.9415715 0.0153221 1040.43 <2e-16 ***
ORIGIN_SZ1136 13.9627811 0.0229093 609.48 <2e-16 ***
ORIGIN_SZ1138 13.2037742 0.0416333 317.14 <2e-16 ***
ORIGIN_SZ1139 15.4167264 0.0092889 1659.70 <2e-16 ***
ORIGIN_SZ1141 15.0360850 0.0126151 1191.91 <2e-16 ***
ORIGIN_SZ1148 13.5748855 0.0672193 201.95 <2e-16 ***
ORIGIN_SZ1149 15.0791558 0.0229876 655.97 <2e-16 ***
ORIGIN_SZ1150 16.2855386 0.0079447 2049.88 <2e-16 ***
ORIGIN_SZ1151 15.3582117 0.0135643 1132.26 <2e-16 ***
ORIGIN_SZ1158 13.8998961 0.0207454 670.02 <2e-16 ***
ORIGIN_SZ1159 14.9926805 0.0110821 1352.88 <2e-16 ***
ORIGIN_SZ1160 15.8790377 0.0075287 2109.15 <2e-16 ***
ORIGIN_SZ1171 16.6072668 0.0083655 1985.21 <2e-16 ***
ORIGIN_SZ1172 16.6874063 0.0072017 2317.16 <2e-16 ***
ORIGIN_SZ1173 14.7019854 0.0219763 668.99 <2e-16 ***
ORIGIN_SZ1174 11.7840329 0.2500211 47.13 <2e-16 ***
ORIGIN_SZ1178 14.6744515 0.0137059 1070.67 <2e-16 ***
ORIGIN_SZ1179 15.1569004 0.0102417 1479.92 <2e-16 ***
ORIGIN_SZ1180 15.8217666 0.0076215 2075.95 <2e-16 ***
ORIGIN_SZ1181 14.8320499 0.0121483 1220.91 <2e-16 ***
ORIGIN_SZ1183 14.2485588 0.0198987 716.05 <2e-16 ***
ORIGIN_SZ1190 13.2554271 0.0713408 185.80 <2e-16 ***
ORIGIN_SZ1192 16.1399854 0.0104477 1544.83 <2e-16 ***
ORIGIN_SZ1193 15.5155521 0.0113983 1361.21 <2e-16 ***
ORIGIN_SZ1194 14.7597132 0.0231139 638.56 <2e-16 ***
ORIGIN_SZ1200 14.5887416 0.0141517 1030.88 <2e-16 ***
ORIGIN_SZ1201 15.1733548 0.0102789 1476.17 <2e-16 ***
ORIGIN_SZ1203 15.3135542 0.0105726 1448.42 <2e-16 ***
ORIGIN_SZ1204 14.2864261 0.0178663 799.63 <2e-16 ***
ORIGIN_SZ1211 14.6746695 0.0463676 316.49 <2e-16 ***
ORIGIN_SZ1214 16.1406442 0.0091659 1760.94 <2e-16 ***
ORIGIN_SZ1215 14.0992543 0.0569978 247.37 <2e-16 ***
ORIGIN_SZ1216 14.2341886 0.0392631 362.53 <2e-16 ***
ORIGIN_SZ1220 15.4617819 0.0092665 1668.57 <2e-16 ***
ORIGIN_SZ1221 15.3176049 0.0088374 1733.26 <2e-16 ***
ORIGIN_SZ1222 15.1878051 0.0181221 838.08 <2e-16 ***
ORIGIN_SZ1223 14.2114286 0.0187550 757.74 <2e-16 ***
ORIGIN_SZ1224 14.4397810 0.0158946 908.47 <2e-16 ***
ORIGIN_SZ1231 13.5328698 0.0663222 204.05 <2e-16 ***
ORIGIN_SZ1232 14.4167133 0.0582521 247.49 <2e-16 ***
ORIGIN_SZ1235 14.0423707 0.0249757 562.24 <2e-16 ***
ORIGIN_SZ1236 14.6300171 0.0203411 719.23 <2e-16 ***
ORIGIN_SZ1241 14.5044303 0.0155848 930.68 <2e-16 ***
ORIGIN_SZ1242 14.6422056 0.0129363 1131.87 <2e-16 ***
ORIGIN_SZ1243 15.3653016 0.0087688 1752.26 <2e-16 ***
ORIGIN_SZ1246 14.9891797 0.0117892 1271.44 <2e-16 ***
ORIGIN_SZ1256 14.8985842 0.0165496 900.24 <2e-16 ***
ORIGIN_SZ1257 15.9234906 0.0112516 1415.22 <2e-16 ***
ORIGIN_SZ1258 14.9628527 0.0199634 749.51 <2e-16 ***
ORIGIN_SZ1262 14.1827295 0.0175103 809.96 <2e-16 ***
ORIGIN_SZ1263 15.6231572 0.0075547 2068.01 <2e-16 ***
ORIGIN_SZ1264 14.5502516 0.0161429 901.34 <2e-16 ***
ORIGIN_SZ1265 14.4706438 0.0161700 894.90 <2e-16 ***
ORIGIN_SZ1266 14.8963782 0.0141381 1053.63 <2e-16 ***
ORIGIN_SZ1267 14.4550799 0.0237579 608.43 <2e-16 ***
ORIGIN_SZ1272 12.1395848 0.1098244 110.54 <2e-16 ***
ORIGIN_SZ1273 14.7587325 0.0214139 689.21 <2e-16 ***
ORIGIN_SZ1277 16.2461192 0.0083460 1946.58 <2e-16 ***
ORIGIN_SZ1278 14.6103330 0.0199997 730.53 <2e-16 ***
ORIGIN_SZ128 16.3527808 0.0300670 543.88 <2e-16 ***
ORIGIN_SZ1283 16.3843652 0.0067056 2443.37 <2e-16 ***
ORIGIN_SZ1284 15.4393080 0.0087339 1767.75 <2e-16 ***
ORIGIN_SZ1285 15.9586004 0.0068919 2315.56 <2e-16 ***
ORIGIN_SZ1286 14.5900822 0.0161669 902.47 <2e-16 ***
ORIGIN_SZ1289 13.7718026 0.0386504 356.32 <2e-16 ***
ORIGIN_SZ129 15.4949105 0.1796524 86.25 <2e-16 ***
ORIGIN_SZ1293 13.3887163 0.0754731 177.40 <2e-16 ***
ORIGIN_SZ1294 15.6526167 0.0139965 1118.32 <2e-16 ***
ORIGIN_SZ1295 14.4342720 0.0259119 557.05 <2e-16 ***
ORIGIN_SZ1298 15.0564686 0.0147162 1023.12 <2e-16 ***
ORIGIN_SZ1299 15.9098023 0.0123491 1288.33 <2e-16 ***
ORIGIN_SZ130 14.0375580 0.0728188 192.77 <2e-16 ***
ORIGIN_SZ1304 15.7776922 0.0080989 1948.13 <2e-16 ***
ORIGIN_SZ1305 15.4350282 0.0077548 1990.38 <2e-16 ***
ORIGIN_SZ1307 12.8415287 0.0397271 323.24 <2e-16 ***
ORIGIN_SZ1308 15.0440705 0.0113951 1320.22 <2e-16 ***
ORIGIN_SZ131 14.5698704 0.0554039 262.98 <2e-16 ***
ORIGIN_SZ1310 12.3887466 0.1021278 121.31 <2e-16 ***
ORIGIN_SZ1316 13.1290904 0.0480364 273.32 <2e-16 ***
ORIGIN_SZ1317 14.0575098 0.0247857 567.16 <2e-16 ***
ORIGIN_SZ1318 13.3179431 0.0382347 348.32 <2e-16 ***
ORIGIN_SZ1319 16.6022505 0.0071648 2317.19 <2e-16 ***
ORIGIN_SZ132 13.5960692 0.0809184 168.02 <2e-16 ***
ORIGIN_SZ1320 15.1637736 0.0183031 828.48 <2e-16 ***
ORIGIN_SZ1325 13.6264907 0.0246319 553.21 <2e-16 ***
ORIGIN_SZ1326 15.3677832 0.0085065 1806.58 <2e-16 ***
ORIGIN_SZ1327 15.2793003 0.0086401 1768.41 <2e-16 ***
ORIGIN_SZ1328 14.6123693 0.0122812 1189.82 <2e-16 ***
ORIGIN_SZ1329 14.9087791 0.0152253 979.21 <2e-16 ***
ORIGIN_SZ133 13.8452904 0.0641089 215.97 <2e-16 ***
ORIGIN_SZ1330 14.4159497 0.0189987 758.79 <2e-16 ***
ORIGIN_SZ1331 11.6283543 0.1690689 68.78 <2e-16 ***
ORIGIN_SZ1333 14.2353986 0.0215166 661.60 <2e-16 ***
ORIGIN_SZ1334 14.5971310 0.0195041 748.41 <2e-16 ***
ORIGIN_SZ1335 14.8029153 0.0198129 747.13 <2e-16 ***
ORIGIN_SZ1336 12.9438178 0.1132914 114.25 <2e-16 ***
ORIGIN_SZ1337 12.7194163 0.0640039 198.73 <2e-16 ***
ORIGIN_SZ1338 11.9004843 0.0845894 140.69 <2e-16 ***
ORIGIN_SZ1339 16.8284017 0.0063131 2665.62 <2e-16 ***
ORIGIN_SZ134 13.6319368 0.0917297 148.61 <2e-16 ***
ORIGIN_SZ1340 15.7643148 0.0118491 1330.43 <2e-16 ***
ORIGIN_SZ1341 10.6316733 0.7071178 15.04 <2e-16 ***
ORIGIN_SZ1346 15.3595732 0.0106784 1438.37 <2e-16 ***
ORIGIN_SZ1347 16.2212946 0.0061056 2656.80 <2e-16 ***
ORIGIN_SZ1348 15.0292019 0.0088133 1705.29 <2e-16 ***
ORIGIN_SZ1349 15.4882478 0.0083569 1853.34 <2e-16 ***
ORIGIN_SZ1350 14.1352596 0.0220538 640.95 <2e-16 ***
ORIGIN_SZ1353 15.2098529 0.0114095 1333.09 <2e-16 ***
ORIGIN_SZ1354 13.9238531 0.0236857 587.86 <2e-16 ***
ORIGIN_SZ1355 14.8686021 0.0153374 969.43 <2e-16 ***
ORIGIN_SZ1357 13.4364831 0.0458068 293.33 <2e-16 ***
ORIGIN_SZ1358 15.3232573 0.0133440 1148.32 <2e-16 ***
ORIGIN_SZ1359 15.5808892 0.0106955 1456.77 <2e-16 ***
ORIGIN_SZ1360 15.5087357 0.0116051 1336.37 <2e-16 ***
ORIGIN_SZ1361 16.5918509 0.0091640 1810.55 <2e-16 ***
ORIGIN_SZ1362 13.0003652 0.0855145 152.03 <2e-16 ***
ORIGIN_SZ1368 14.2652451 0.0133143 1071.42 <2e-16 ***
ORIGIN_SZ1369 13.8633597 0.0151646 914.20 <2e-16 ***
ORIGIN_SZ1370 15.9422920 0.0062312 2558.47 <2e-16 ***
ORIGIN_SZ1371 14.5108378 0.0163009 890.19 <2e-16 ***
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ORIGIN_SZ876 12.4603236 0.0822715 151.45 <2e-16 ***
ORIGIN_SZ877 14.6926381 0.0290314 506.10 <2e-16 ***
ORIGIN_SZ88 15.8997807 0.0231652 686.37 <2e-16 ***
ORIGIN_SZ887 14.1377979 0.0233994 604.20 <2e-16 ***
ORIGIN_SZ888 14.9668033 0.0155085 965.07 <2e-16 ***
ORIGIN_SZ889 12.6517437 0.0534942 236.51 <2e-16 ***
ORIGIN_SZ89 12.2938875 0.1796375 68.44 <2e-16 ***
ORIGIN_SZ890 15.9525403 0.0078114 2042.21 <2e-16 ***
ORIGIN_SZ891 15.0765504 0.0219579 686.61 <2e-16 ***
ORIGIN_SZ893 16.1706351 0.0076046 2126.42 <2e-16 ***
ORIGIN_SZ894 13.8640928 0.0255834 541.92 <2e-16 ***
ORIGIN_SZ895 13.9650201 0.0281490 496.11 <2e-16 ***
ORIGIN_SZ896 13.0334530 0.0610771 213.39 <2e-16 ***
ORIGIN_SZ897 13.2146530 0.0673556 196.19 <2e-16 ***
ORIGIN_SZ898 14.1888920 0.0408014 347.75 <2e-16 ***
ORIGIN_SZ90 14.5607795 0.1005725 144.78 <2e-16 ***
ORIGIN_SZ908 14.6561646 0.0266372 550.22 <2e-16 ***
ORIGIN_SZ909 15.3104347 0.0109801 1394.38 <2e-16 ***
ORIGIN_SZ910 12.3102039 0.0574673 214.21 <2e-16 ***
ORIGIN_SZ911 15.1414435 0.0129015 1173.62 <2e-16 ***
ORIGIN_SZ912 15.8428381 0.0082539 1919.43 <2e-16 ***
ORIGIN_SZ915 15.7858628 0.0089398 1765.79 <2e-16 ***
ORIGIN_SZ917 15.9485266 0.0117520 1357.09 <2e-16 ***
ORIGIN_SZ918 13.6174307 0.0444290 306.50 <2e-16 ***
ORIGIN_SZ919 14.5143344 0.0263129 551.61 <2e-16 ***
ORIGIN_SZ928 14.4974164 0.0227624 636.90 <2e-16 ***
ORIGIN_SZ929 15.4744702 0.0096318 1606.60 <2e-16 ***
ORIGIN_SZ930 16.4730396 0.0060235 2734.79 <2e-16 ***
ORIGIN_SZ931 13.0005491 0.0420049 309.50 <2e-16 ***
ORIGIN_SZ932 13.4212779 0.0424873 315.89 <2e-16 ***
ORIGIN_SZ933 15.3897198 0.0122343 1257.92 <2e-16 ***
ORIGIN_SZ934 12.6362667 0.0463204 272.80 <2e-16 ***
ORIGIN_SZ935 17.2515974 0.0052986 3255.86 <2e-16 ***
ORIGIN_SZ938 11.8907810 0.1826057 65.12 <2e-16 ***
ORIGIN_SZ939 16.8705581 0.0073711 2288.75 <2e-16 ***
ORIGIN_SZ940 13.4575628 0.1222120 110.12 <2e-16 ***
ORIGIN_SZ949 14.6120242 0.0195090 748.99 <2e-16 ***
ORIGIN_SZ950 16.5723217 0.0076145 2176.41 <2e-16 ***
ORIGIN_SZ951 16.8093561 0.0055897 3007.22 <2e-16 ***
ORIGIN_SZ952 14.4268859 0.0314233 459.12 <2e-16 ***
ORIGIN_SZ953 14.5906109 0.0189809 768.70 <2e-16 ***
ORIGIN_SZ954 13.1917954 0.0331139 398.38 <2e-16 ***
ORIGIN_SZ955 15.7361311 0.0095658 1645.04 <2e-16 ***
ORIGIN_SZ956 13.8128917 0.0232756 593.45 <2e-16 ***
ORIGIN_SZ957 15.9686291 0.0100832 1583.69 <2e-16 ***
ORIGIN_SZ959 13.3442839 0.0684411 194.97 <2e-16 ***
ORIGIN_SZ961 13.5557445 0.0448593 302.18 <2e-16 ***
ORIGIN_SZ962 22.0953950 0.0060081 3677.58 <2e-16 ***
ORIGIN_SZ970 15.0577394 0.0130321 1155.44 <2e-16 ***
ORIGIN_SZ971 15.7903098 0.0078110 2021.55 <2e-16 ***
ORIGIN_SZ972 15.6663454 0.0094224 1662.67 <2e-16 ***
ORIGIN_SZ974 14.9416181 0.0146258 1021.59 <2e-16 ***
ORIGIN_SZ975 14.3062522 0.0198409 721.05 <2e-16 ***
ORIGIN_SZ976 14.3381365 0.0197690 725.28 <2e-16 ***
ORIGIN_SZ977 16.1289917 0.0076821 2099.55 <2e-16 ***
ORIGIN_SZ978 15.8699511 0.0135393 1172.14 <2e-16 ***
ORIGIN_SZ982 13.7058893 0.0335654 408.33 <2e-16 ***
ORIGIN_SZ983 17.8136822 0.0075354 2364.01 <2e-16 ***
ORIGIN_SZ984 19.7793698 0.0066796 2961.16 <2e-16 ***
ORIGIN_SZ991 15.1433400 0.0134885 1122.68 <2e-16 ***
ORIGIN_SZ992 15.3520267 0.0114321 1342.88 <2e-16 ***
ORIGIN_SZ993 14.5899841 0.0152310 957.92 <2e-16 ***
ORIGIN_SZ994 14.3168785 0.0185980 769.81 <2e-16 ***
ORIGIN_SZ995 15.8579526 0.0087774 1806.68 <2e-16 ***
ORIGIN_SZ996 14.8048932 0.0156119 948.31 <2e-16 ***
ORIGIN_SZ997 14.0468579 0.0437726 320.90 <2e-16 ***
ORIGIN_SZ998 16.2337342 0.0080936 2005.76 <2e-16 ***
ORIGIN_SZ999 16.3072010 0.0102976 1583.59 <2e-16 ***
log(SCHOOL_COUNT) 0.2593888 0.0012140 213.67 <2e-16 ***
log(ENTERTN_COUNT) -0.0559950 0.0012458 -44.95 <2e-16 ***
log(RTSS_COUNT) 0.7053466 0.0014582 483.72 <2e-16 ***
log(LR_COUNT) -0.0186901 0.0006064 -30.82 <2e-16 ***
log(RETAILS_COUNT) 0.3041548 0.0002912 1044.38 <2e-16 ***
log(DIST) -1.5020359 0.0004760 -3155.86 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 81537309 on 61828 degrees of freedom
Residual deviance: 9621538 on 61001 degrees of freedom
AIC: 9912398
Number of Fisher Scoring iterations: 7CalcRSquared <- function(observed, estimated){
r <- cor(observed, estimated)
R2 <- r^2
R2
}CalcRSquared(orcSIM_Poisson$data$TRIPS, orcSIM_Poisson$fitted.values)[1] 0.4426548Conclusion of Origin_Constrained model
Currently, the OM model yields an R-squared value of 44%, indicating that the model explains approximately 44% of the variance in the response variable TRIPS. The significant p-values suggest that the model is effective, as these values indicate statistically significant impacts of the explanatory variables on the response variable. However, given that the fit is only 44%, it is necessary to explore comparisons with different models. This suggests that there might be unexplained variability, possibly due to important variables not included in the model or complex nonlinear relationships not captured by the current model. Therefore, further analysis is required to enhance the explanatory power of the model.
Doubly_Constrained model
dbcSIM_Poisson <- glm(formula = TRIPS ~
ORIGIN_SZ +
DESTIN_SZ +
log(DIST),
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)
summary(dbcSIM_Poisson)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST), family = poisson(link = "log"),
data = inter_zonal_flow, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 13.0640549 0.0721898 180.968 < 2e-16 ***
ORIGIN_SZ1003 2.4306487 0.0490713 49.533 < 2e-16 ***
ORIGIN_SZ1004 2.4521733 0.0491255 49.917 < 2e-16 ***
ORIGIN_SZ1011 -0.0404507 0.0609743 -0.663 0.507070
ORIGIN_SZ1012 0.9269684 0.0541662 17.113 < 2e-16 ***
ORIGIN_SZ1013 0.4939063 0.0524185 9.422 < 2e-16 ***
ORIGIN_SZ1014 0.5392816 0.0518772 10.395 < 2e-16 ***
ORIGIN_SZ1015 -0.1732128 0.0551950 -3.138 0.001700 **
ORIGIN_SZ1016 2.0935168 0.0493366 42.433 < 2e-16 ***
ORIGIN_SZ1018 1.1021795 0.0525039 20.992 < 2e-16 ***
ORIGIN_SZ1019 2.8326657 0.0491510 57.632 < 2e-16 ***
ORIGIN_SZ1023 0.9666893 0.0522211 18.511 < 2e-16 ***
ORIGIN_SZ1024 2.0741696 0.0493875 41.998 < 2e-16 ***
ORIGIN_SZ1025 -0.7800208 0.0724034 -10.773 < 2e-16 ***
ORIGIN_SZ1033 0.9135244 0.0515134 17.734 < 2e-16 ***
ORIGIN_SZ1034 1.4397837 0.0499966 28.798 < 2e-16 ***
ORIGIN_SZ1035 1.6289124 0.0497139 32.766 < 2e-16 ***
ORIGIN_SZ1036 1.6945172 0.0497184 34.082 < 2e-16 ***
ORIGIN_SZ1037 1.5688715 0.0495390 31.669 < 2e-16 ***
ORIGIN_SZ1043 1.6838454 0.0525854 32.021 < 2e-16 ***
ORIGIN_SZ1045 2.1033352 0.0491582 42.787 < 2e-16 ***
ORIGIN_SZ1046 2.0134750 0.0494993 40.677 < 2e-16 ***
ORIGIN_SZ1053 1.4843989 0.0503564 29.478 < 2e-16 ***
ORIGIN_SZ1054 0.6660582 0.0517640 12.867 < 2e-16 ***
ORIGIN_SZ1055 1.8741206 0.0494812 37.875 < 2e-16 ***
ORIGIN_SZ1056 0.9813962 0.0509245 19.272 < 2e-16 ***
ORIGIN_SZ1064 -0.7820504 0.1861739 -4.201 2.66e-05 ***
ORIGIN_SZ1066 2.1799422 0.0491284 44.372 < 2e-16 ***
ORIGIN_SZ1067 0.8369846 0.0531667 15.743 < 2e-16 ***
ORIGIN_SZ1074 1.3936197 0.0505324 27.579 < 2e-16 ***
ORIGIN_SZ1075 -0.4751740 0.0600533 -7.913 2.52e-15 ***
ORIGIN_SZ1076 0.7801192 0.0508528 15.341 < 2e-16 ***
ORIGIN_SZ1077 0.6373516 0.0520763 12.239 < 2e-16 ***
ORIGIN_SZ1079 1.6816491 0.0496877 33.844 < 2e-16 ***
ORIGIN_SZ1085 -1.9195106 0.1151501 -16.670 < 2e-16 ***
ORIGIN_SZ1087 1.1040121 0.0500637 22.052 < 2e-16 ***
ORIGIN_SZ1088 -0.1389263 0.0538845 -2.578 0.009931 **
ORIGIN_SZ109 -0.2204871 0.1161062 -1.899 0.057563 .
ORIGIN_SZ1094 -0.8681177 0.0958703 -9.055 < 2e-16 ***
ORIGIN_SZ1095 -0.3178508 0.0724997 -4.384 1.16e-05 ***
ORIGIN_SZ1096 0.3740676 0.0707495 5.287 1.24e-07 ***
ORIGIN_SZ1097 2.3792386 0.0490412 48.515 < 2e-16 ***
ORIGIN_SZ1098 -0.0306528 0.0579699 -0.529 0.596964
ORIGIN_SZ1099 1.4345640 0.0499274 28.733 < 2e-16 ***
ORIGIN_SZ110 -0.4690077 0.0951868 -4.927 8.34e-07 ***
ORIGIN_SZ1105 2.7510717 0.0519597 52.946 < 2e-16 ***
ORIGIN_SZ1106 -2.0529149 0.1552107 -13.227 < 2e-16 ***
ORIGIN_SZ1107 -0.1116540 0.0618571 -1.805 0.071070 .
ORIGIN_SZ1108 3.8127834 0.0487472 78.215 < 2e-16 ***
ORIGIN_SZ1109 0.7227322 0.0532247 13.579 < 2e-16 ***
ORIGIN_SZ111 4.5907097 0.0527038 87.104 < 2e-16 ***
ORIGIN_SZ1116 0.5893302 0.0524259 11.241 < 2e-16 ***
ORIGIN_SZ1117 0.4200775 0.0540593 7.771 7.81e-15 ***
ORIGIN_SZ1118 -0.3552376 0.0603873 -5.883 4.04e-09 ***
ORIGIN_SZ1119 1.1759389 0.0503909 23.336 < 2e-16 ***
ORIGIN_SZ112 -1.3671596 0.1720780 -7.945 1.94e-15 ***
ORIGIN_SZ1120 0.5617258 0.0539325 10.415 < 2e-16 ***
ORIGIN_SZ1129 1.7497468 0.0495227 35.332 < 2e-16 ***
ORIGIN_SZ1130 1.8229020 0.0492936 36.980 < 2e-16 ***
ORIGIN_SZ1131 1.9970300 0.0509138 39.224 < 2e-16 ***
ORIGIN_SZ1136 0.3385629 0.0536272 6.313 2.73e-10 ***
ORIGIN_SZ1138 -0.4399362 0.0639880 -6.875 6.19e-12 ***
ORIGIN_SZ1139 1.7545048 0.0493593 35.546 < 2e-16 ***
ORIGIN_SZ1141 1.3904501 0.0500601 27.776 < 2e-16 ***
ORIGIN_SZ1148 -0.4949462 0.0827557 -5.981 2.22e-09 ***
ORIGIN_SZ1149 0.5954274 0.0537901 11.069 < 2e-16 ***
ORIGIN_SZ1150 1.8525219 0.0491951 37.657 < 2e-16 ***
ORIGIN_SZ1151 1.2930718 0.0504137 25.649 < 2e-16 ***
ORIGIN_SZ1158 0.3415657 0.0527487 6.475 9.46e-11 ***
ORIGIN_SZ1159 1.3066218 0.0497217 26.279 < 2e-16 ***
ORIGIN_SZ1160 2.2395833 0.0490521 45.657 < 2e-16 ***
ORIGIN_SZ1171 2.4454855 0.0492852 49.619 < 2e-16 ***
ORIGIN_SZ1172 2.6264335 0.0490833 53.510 < 2e-16 ***
ORIGIN_SZ1173 0.7432981 0.0533195 13.940 < 2e-16 ***
ORIGIN_SZ1174 -1.2890114 0.2550009 -5.055 4.31e-07 ***
ORIGIN_SZ1178 1.0788689 0.0503763 21.416 < 2e-16 ***
ORIGIN_SZ1179 1.5204293 0.0495529 30.683 < 2e-16 ***
ORIGIN_SZ1180 2.1232024 0.0490677 43.271 < 2e-16 ***
ORIGIN_SZ1181 1.1316119 0.0499676 22.647 < 2e-16 ***
ORIGIN_SZ1183 0.5744784 0.0523770 10.968 < 2e-16 ***
ORIGIN_SZ1190 -0.5991538 0.0862238 -6.949 3.68e-12 ***
ORIGIN_SZ1192 1.7538205 0.0496926 35.293 < 2e-16 ***
ORIGIN_SZ1193 1.6703040 0.0498863 33.482 < 2e-16 ***
ORIGIN_SZ1194 0.9783056 0.0538030 18.183 < 2e-16 ***
ORIGIN_SZ1200 0.9121428 0.0505287 18.052 < 2e-16 ***
ORIGIN_SZ1201 1.4751211 0.0495641 29.762 < 2e-16 ***
ORIGIN_SZ1203 1.7290357 0.0496032 34.857 < 2e-16 ***
ORIGIN_SZ1204 0.6797348 0.0516457 13.162 < 2e-16 ***
ORIGIN_SZ1211 1.1163721 0.0676319 16.507 < 2e-16 ***
ORIGIN_SZ1214 2.0792287 0.0494146 42.077 < 2e-16 ***
ORIGIN_SZ1215 -0.3909598 0.0749276 -5.218 1.81e-07 ***
ORIGIN_SZ1216 0.3953879 0.0625010 6.326 2.51e-10 ***
ORIGIN_SZ1220 1.7868423 0.0493531 36.205 < 2e-16 ***
ORIGIN_SZ1221 1.6295953 0.0492794 33.069 < 2e-16 ***
ORIGIN_SZ1222 1.2146433 0.0518078 23.445 < 2e-16 ***
ORIGIN_SZ1223 0.5259056 0.0519751 10.118 < 2e-16 ***
ORIGIN_SZ1224 0.8493675 0.0510110 16.651 < 2e-16 ***
ORIGIN_SZ1231 -0.3699644 0.0821744 -4.502 6.73e-06 ***
ORIGIN_SZ1232 0.5607886 0.0757912 7.399 1.37e-13 ***
ORIGIN_SZ1235 0.0370091 0.0546189 0.678 0.498033
ORIGIN_SZ1236 1.2469919 0.0527064 23.659 < 2e-16 ***
ORIGIN_SZ1241 0.5702658 0.0509280 11.197 < 2e-16 ***
ORIGIN_SZ1242 0.9043507 0.0501950 18.017 < 2e-16 ***
ORIGIN_SZ1243 1.6982346 0.0492693 34.468 < 2e-16 ***
ORIGIN_SZ1246 1.4453277 0.0498715 28.981 < 2e-16 ***
ORIGIN_SZ1256 0.8934195 0.0512998 17.416 < 2e-16 ***
ORIGIN_SZ1257 2.0942339 0.0499116 41.959 < 2e-16 ***
ORIGIN_SZ1258 1.3745672 0.0525336 26.165 < 2e-16 ***
ORIGIN_SZ1262 0.2724068 0.0515773 5.282 1.28e-07 ***
ORIGIN_SZ1263 1.8999778 0.0490603 38.727 < 2e-16 ***
ORIGIN_SZ1264 0.7582731 0.0511258 14.832 < 2e-16 ***
ORIGIN_SZ1265 0.8419338 0.0510972 16.477 < 2e-16 ***
ORIGIN_SZ1266 1.2525636 0.0504895 24.808 < 2e-16 ***
ORIGIN_SZ1267 0.7819989 0.0539920 14.484 < 2e-16 ***
ORIGIN_SZ1272 -1.8725507 0.1200853 -15.593 < 2e-16 ***
ORIGIN_SZ1273 0.9324405 0.0529746 17.602 < 2e-16 ***
ORIGIN_SZ1277 2.3327178 0.0492803 47.336 < 2e-16 ***
ORIGIN_SZ1278 0.8629043 0.0525641 16.416 < 2e-16 ***
ORIGIN_SZ128 4.0588740 0.0615930 65.898 < 2e-16 ***
ORIGIN_SZ1283 2.7647584 0.0489267 56.508 < 2e-16 ***
ORIGIN_SZ1284 1.6575326 0.0492724 33.640 < 2e-16 ***
ORIGIN_SZ1285 2.3328366 0.0489702 47.638 < 2e-16 ***
ORIGIN_SZ1286 0.8673920 0.0511099 16.971 < 2e-16 ***
ORIGIN_SZ1289 0.0489966 0.0620199 0.790 0.429519
ORIGIN_SZ129 0.7278825 0.1868936 3.895 9.83e-05 ***
ORIGIN_SZ1293 -0.6245556 0.0896787 -6.964 3.30e-12 ***
ORIGIN_SZ1294 2.0506305 0.0503780 40.705 < 2e-16 ***
ORIGIN_SZ1295 0.6266412 0.0549903 11.395 < 2e-16 ***
ORIGIN_SZ1298 1.0025731 0.0507373 19.760 < 2e-16 ***
ORIGIN_SZ1299 1.8424033 0.0501640 36.728 < 2e-16 ***
ORIGIN_SZ130 0.0469286 0.0902259 0.520 0.602978
ORIGIN_SZ1304 1.9136034 0.0491773 38.912 < 2e-16 ***
ORIGIN_SZ1305 1.7099926 0.0490980 34.828 < 2e-16 ***
ORIGIN_SZ1307 -0.8411833 0.0627043 -13.415 < 2e-16 ***
ORIGIN_SZ1308 1.4473470 0.0497829 29.073 < 2e-16 ***
ORIGIN_SZ131 -0.6673841 0.0782627 -8.527 < 2e-16 ***
ORIGIN_SZ1310 -1.3899548 0.1130835 -12.291 < 2e-16 ***
ORIGIN_SZ1316 -0.7845915 0.0682576 -11.495 < 2e-16 ***
ORIGIN_SZ1317 0.0636179 0.0544694 1.168 0.242824
ORIGIN_SZ1318 -0.8168545 0.0617912 -13.220 < 2e-16 ***
ORIGIN_SZ1319 2.7057767 0.0490922 55.116 < 2e-16 ***
ORIGIN_SZ132 -0.3532106 0.0966122 -3.656 0.000256 ***
ORIGIN_SZ1320 1.3169516 0.0519255 25.362 < 2e-16 ***
ORIGIN_SZ1325 -0.3967623 0.0544044 -7.293 3.03e-13 ***
ORIGIN_SZ1326 1.6144888 0.0492260 32.797 < 2e-16 ***
ORIGIN_SZ1327 1.5665861 0.0492485 31.810 < 2e-16 ***
ORIGIN_SZ1328 0.8839024 0.0500116 17.674 < 2e-16 ***
ORIGIN_SZ1329 1.1846105 0.0508193 23.310 < 2e-16 ***
ORIGIN_SZ133 -0.6401798 0.0819914 -7.808 5.82e-15 ***
ORIGIN_SZ1330 0.8857699 0.0520813 17.007 < 2e-16 ***
ORIGIN_SZ1331 -1.8313780 0.1759375 -10.409 < 2e-16 ***
ORIGIN_SZ1333 0.6108447 0.0530453 11.516 < 2e-16 ***
ORIGIN_SZ1334 0.9964997 0.0522597 19.068 < 2e-16 ***
ORIGIN_SZ1335 1.1088582 0.0523278 21.191 < 2e-16 ***
ORIGIN_SZ1336 -1.2038367 0.1232717 -9.766 < 2e-16 ***
ORIGIN_SZ1337 -1.4627843 0.0803077 -18.215 < 2e-16 ***
ORIGIN_SZ1338 -2.1871734 0.0975331 -22.425 < 2e-16 ***
ORIGIN_SZ1339 2.9173023 0.0489174 59.637 < 2e-16 ***
ORIGIN_SZ134 1.0672255 0.1085679 9.830 < 2e-16 ***
ORIGIN_SZ1340 1.6807304 0.0499619 33.640 < 2e-16 ***
ORIGIN_SZ1341 -3.7685794 0.7087870 -5.317 1.06e-07 ***
ORIGIN_SZ1346 1.6533200 0.0496495 33.300 < 2e-16 ***
ORIGIN_SZ1347 2.6657092 0.0488734 54.543 < 2e-16 ***
ORIGIN_SZ1348 1.4502944 0.0492741 29.433 < 2e-16 ***
ORIGIN_SZ1349 1.8551470 0.0491976 37.708 < 2e-16 ***
ORIGIN_SZ1350 0.5488517 0.0532954 10.298 < 2e-16 ***
ORIGIN_SZ1353 1.5726898 0.0498107 31.573 < 2e-16 ***
ORIGIN_SZ1354 0.2515158 0.0539677 4.660 3.15e-06 ***
ORIGIN_SZ1355 1.2351213 0.0508311 24.299 < 2e-16 ***
ORIGIN_SZ1357 -0.5660007 0.0666995 -8.486 < 2e-16 ***
ORIGIN_SZ1358 1.3771382 0.0502943 27.382 < 2e-16 ***
ORIGIN_SZ1359 1.4608057 0.0496909 29.398 < 2e-16 ***
ORIGIN_SZ1360 1.3268673 0.0499090 26.586 < 2e-16 ***
ORIGIN_SZ1361 2.3196150 0.0494488 46.909 < 2e-16 ***
ORIGIN_SZ1362 -0.9898456 0.0983866 -10.061 < 2e-16 ***
ORIGIN_SZ1368 0.6340436 0.0502813 12.610 < 2e-16 ***
ORIGIN_SZ1369 0.2251042 0.0508009 4.431 9.38e-06 ***
ORIGIN_SZ1370 2.3400448 0.0488712 47.882 < 2e-16 ***
ORIGIN_SZ1371 0.8263613 0.0511520 16.155 < 2e-16 ***
ORIGIN_SZ1372 -0.4762815 0.0571270 -8.337 < 2e-16 ***
ORIGIN_SZ1373 -1.0716526 0.0735134 -14.578 < 2e-16 ***
ORIGIN_SZ1374 0.2628847 0.0523267 5.024 5.06e-07 ***
ORIGIN_SZ1375 1.4477227 0.0507333 28.536 < 2e-16 ***
ORIGIN_SZ1376 0.6819754 0.0540488 12.618 < 2e-16 ***
ORIGIN_SZ1379 -1.1916197 0.0791632 -15.053 < 2e-16 ***
ORIGIN_SZ1380 2.8295850 0.0489067 57.857 < 2e-16 ***
ORIGIN_SZ1381 2.6893987 0.0489828 54.905 < 2e-16 ***
ORIGIN_SZ1382 1.8664045 0.0498853 37.414 < 2e-16 ***
ORIGIN_SZ1383 -0.6647541 0.0649118 -10.241 < 2e-16 ***
ORIGIN_SZ1388 1.0651564 0.0498305 21.376 < 2e-16 ***
ORIGIN_SZ1389 0.6876658 0.0499902 13.756 < 2e-16 ***
ORIGIN_SZ1390 1.0779273 0.0495143 21.770 < 2e-16 ***
ORIGIN_SZ1391 1.0025737 0.0498391 20.116 < 2e-16 ***
ORIGIN_SZ1392 0.7308568 0.0530989 13.764 < 2e-16 ***
ORIGIN_SZ1393 -0.6110093 0.0566686 -10.782 < 2e-16 ***
ORIGIN_SZ1394 1.4863190 0.0495856 29.975 < 2e-16 ***
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ORIGIN_SZ1710 1.9425579 0.0492827 39.417 < 2e-16 ***
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ORIGIN_SZ2002 1.8202086 0.0491043 37.068 < 2e-16 ***
ORIGIN_SZ2003 1.7524529 0.0493239 35.529 < 2e-16 ***
ORIGIN_SZ2004 2.4389760 0.0490575 49.717 < 2e-16 ***
ORIGIN_SZ2005 1.7732699 0.0493824 35.909 < 2e-16 ***
ORIGIN_SZ2006 1.2292148 0.0502485 24.463 < 2e-16 ***
ORIGIN_SZ2007 -0.3106531 0.0615652 -5.046 4.51e-07 ***
ORIGIN_SZ2022 1.9297470 0.0496412 38.874 < 2e-16 ***
ORIGIN_SZ2023 2.1244859 0.0490717 43.294 < 2e-16 ***
ORIGIN_SZ2024 1.6956047 0.0492533 34.426 < 2e-16 ***
ORIGIN_SZ2025 1.2769329 0.0494904 25.802 < 2e-16 ***
ORIGIN_SZ2026 -0.0296230 0.0539021 -0.550 0.582614
ORIGIN_SZ2027 2.2240114 0.0492002 45.203 < 2e-16 ***
ORIGIN_SZ2043 1.1367553 0.0505806 22.474 < 2e-16 ***
ORIGIN_SZ2044 1.6134591 0.0493553 32.691 < 2e-16 ***
ORIGIN_SZ2045 -0.9483736 0.0944237 -10.044 < 2e-16 ***
ORIGIN_SZ2046 2.1612934 0.0489480 44.155 < 2e-16 ***
ORIGIN_SZ2047 1.2194295 0.0497829 24.495 < 2e-16 ***
ORIGIN_SZ2048 1.5186376 0.0495032 30.678 < 2e-16 ***
ORIGIN_SZ2049 0.5814792 0.0560634 10.372 < 2e-16 ***
ORIGIN_SZ2064 1.6505073 0.0495939 33.280 < 2e-16 ***
ORIGIN_SZ2065 0.7595061 0.0505254 15.032 < 2e-16 ***
ORIGIN_SZ2066 0.1131691 0.0589556 1.920 0.054913 .
ORIGIN_SZ2067 3.3957652 0.0487488 69.658 < 2e-16 ***
ORIGIN_SZ2068 1.0571465 0.0507914 20.814 < 2e-16 ***
ORIGIN_SZ2069 1.6352794 0.0496300 32.949 < 2e-16 ***
ORIGIN_SZ2085 0.7202811 0.0516528 13.945 < 2e-16 ***
ORIGIN_SZ2086 1.9938654 0.0492821 40.458 < 2e-16 ***
ORIGIN_SZ2087 1.1780046 0.0499732 23.573 < 2e-16 ***
ORIGIN_SZ2088 1.5803103 0.0492100 32.114 < 2e-16 ***
ORIGIN_SZ2089 0.9452998 0.0502465 18.813 < 2e-16 ***
ORIGIN_SZ2090 2.9025919 0.0488709 59.393 < 2e-16 ***
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ORIGIN_SZ2107 0.6699059 0.0507688 13.195 < 2e-16 ***
ORIGIN_SZ2108 1.8785100 0.0493681 38.051 < 2e-16 ***
ORIGIN_SZ2109 1.3227553 0.0494133 26.769 < 2e-16 ***
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ORIGIN_SZ2129 0.2252338 0.0525483 4.286 1.82e-05 ***
ORIGIN_SZ2130 2.0653773 0.0490543 42.104 < 2e-16 ***
ORIGIN_SZ2131 2.1426674 0.0493450 43.422 < 2e-16 ***
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ORIGIN_SZ2148 1.5171068 0.0514238 29.502 < 2e-16 ***
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ORIGIN_SZ2150 1.8225699 0.0494456 36.860 < 2e-16 ***
ORIGIN_SZ2151 2.2172261 0.0490167 45.234 < 2e-16 ***
ORIGIN_SZ2152 2.3665441 0.0490633 48.234 < 2e-16 ***
ORIGIN_SZ2153 1.6945503 0.0499076 33.954 < 2e-16 ***
ORIGIN_SZ216 1.2089823 0.0652916 18.517 < 2e-16 ***
ORIGIN_SZ217 0.8183597 0.0595780 13.736 < 2e-16 ***
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ORIGIN_SZ2174 1.5977217 0.0497747 32.099 < 2e-16 ***
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ORIGIN_SZ2192 0.4426165 0.0527706 8.388 < 2e-16 ***
ORIGIN_SZ2193 1.1419448 0.0503275 22.690 < 2e-16 ***
ORIGIN_SZ2194 1.7462535 0.0494400 35.321 < 2e-16 ***
ORIGIN_SZ2195 0.4464232 0.0641484 6.959 3.42e-12 ***
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ORIGIN_SZ2214 0.4009866 0.0592968 6.762 1.36e-11 ***
ORIGIN_SZ2215 1.4383567 0.0503873 28.546 < 2e-16 ***
ORIGIN_SZ2216 0.3845513 0.0535829 7.177 7.14e-13 ***
ORIGIN_SZ2233 0.1871952 0.0658346 2.843 0.004463 **
ORIGIN_SZ2234 0.8004626 0.0642377 12.461 < 2e-16 ***
ORIGIN_SZ2235 0.7157608 0.0547368 13.076 < 2e-16 ***
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ORIGIN_SZ2237 -0.4130691 0.0823079 -5.019 5.21e-07 ***
ORIGIN_SZ2256 -0.3352698 0.0763179 -4.393 1.12e-05 ***
ORIGIN_SZ2257 0.1027702 0.0610643 1.683 0.092378 .
ORIGIN_SZ2258 0.1548679 0.0559721 2.767 0.005660 **
ORIGIN_SZ2259 0.3673617 0.0758250 4.845 1.27e-06 ***
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ORIGIN_SZ2278 0.1299589 0.0641497 2.026 0.042778 *
ORIGIN_SZ2279 -0.0533265 0.0599053 -0.890 0.373369
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ORIGIN_SZ2319 1.1398874 0.0505221 22.562 < 2e-16 ***
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ORIGIN_SZ2337 3.7351257 0.0518452 72.044 < 2e-16 ***
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ORIGIN_SZ2343 1.0303251 0.0523544 19.680 < 2e-16 ***
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ORIGIN_SZ2384 1.5455085 0.0538966 28.675 < 2e-16 ***
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ORIGIN_SZ2405 1.3904428 0.0542131 25.648 < 2e-16 ***
ORIGIN_SZ2406 0.3400624 0.0680647 4.996 5.85e-07 ***
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ORIGIN_SZ259 0.0234666 0.0722855 0.325 0.745455
ORIGIN_SZ278 3.3136572 0.0598490 55.367 < 2e-16 ***
ORIGIN_SZ279 1.1039544 0.0658049 16.776 < 2e-16 ***
ORIGIN_SZ280 0.2509118 0.0683852 3.669 0.000243 ***
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ORIGIN_SZ299 0.7004433 0.0899145 7.790 6.70e-15 ***
ORIGIN_SZ300 0.1746794 0.0747981 2.335 0.019525 *
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ORIGIN_SZ321 0.5187868 0.1060549 4.892 1.00e-06 ***
ORIGIN_SZ322 -0.2104098 0.0949952 -2.215 0.026763 *
ORIGIN_SZ340 3.0323493 0.0620639 48.858 < 2e-16 ***
ORIGIN_SZ341 1.5946107 0.0682244 23.373 < 2e-16 ***
ORIGIN_SZ342 0.3964489 0.0739214 5.363 8.18e-08 ***
ORIGIN_SZ363 1.6339160 0.0653760 24.993 < 2e-16 ***
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ORIGIN_SZ383 2.0657952 0.0608690 33.938 < 2e-16 ***
ORIGIN_SZ384 -0.2883858 0.0791373 -3.644 0.000268 ***
ORIGIN_SZ385 -1.8321972 0.1512748 -12.112 < 2e-16 ***
ORIGIN_SZ404 2.1542056 0.0688250 31.300 < 2e-16 ***
ORIGIN_SZ405 1.0422314 0.0710342 14.672 < 2e-16 ***
ORIGIN_SZ406 2.6724383 0.0498577 53.601 < 2e-16 ***
ORIGIN_SZ407 0.9846060 0.0581370 16.936 < 2e-16 ***
ORIGIN_SZ408 1.8480599 0.0521200 35.458 < 2e-16 ***
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ORIGIN_SZ426 0.2887056 0.0680402 4.243 2.20e-05 ***
ORIGIN_SZ427 -0.1449570 0.0591900 -2.449 0.014325 *
ORIGIN_SZ428 0.8357102 0.0566283 14.758 < 2e-16 ***
ORIGIN_SZ429 0.8354754 0.0573787 14.561 < 2e-16 ***
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ORIGIN_SZ446 0.7591625 0.0789906 9.611 < 2e-16 ***
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ORIGIN_SZ448 -0.6151542 0.0712329 -8.636 < 2e-16 ***
ORIGIN_SZ449 1.5866385 0.0507136 31.286 < 2e-16 ***
ORIGIN_SZ450 0.6753363 0.0541440 12.473 < 2e-16 ***
ORIGIN_SZ46 0.0149077 0.1038316 0.144 0.885836
ORIGIN_SZ468 1.2138744 0.0608345 19.954 < 2e-16 ***
ORIGIN_SZ469 -0.3097769 0.0599255 -5.169 2.35e-07 ***
ORIGIN_SZ470 2.2693294 0.0495110 45.835 < 2e-16 ***
ORIGIN_SZ471 1.9694079 0.0522754 37.674 < 2e-16 ***
ORIGIN_SZ488 0.2049765 0.0900515 2.276 0.022833 *
ORIGIN_SZ489 -2.4380626 0.2716738 -8.974 < 2e-16 ***
ORIGIN_SZ490 1.1060603 0.0535048 20.672 < 2e-16 ***
ORIGIN_SZ491 0.8267348 0.0511923 16.150 < 2e-16 ***
ORIGIN_SZ493 -2.4401800 0.2098685 -11.627 < 2e-16 ***
ORIGIN_SZ494 1.2669084 0.0599701 21.126 < 2e-16 ***
ORIGIN_SZ509 0.7074668 0.0690155 10.251 < 2e-16 ***
ORIGIN_SZ510 1.0268478 0.0570769 17.991 < 2e-16 ***
ORIGIN_SZ511 -0.0697666 0.0559312 -1.247 0.212263
ORIGIN_SZ512 2.4475768 0.0491162 49.832 < 2e-16 ***
ORIGIN_SZ513 -0.5690416 0.0724316 -7.856 3.96e-15 ***
ORIGIN_SZ514 0.5588751 0.0669061 8.353 < 2e-16 ***
ORIGIN_SZ515 -0.5532178 0.1181041 -4.684 2.81e-06 ***
ORIGIN_SZ530 0.1992727 0.0920644 2.164 0.030427 *
ORIGIN_SZ531 0.9619499 0.0605440 15.888 < 2e-16 ***
ORIGIN_SZ532 0.2629051 0.0569775 4.614 3.95e-06 ***
ORIGIN_SZ533 2.2722218 0.0490868 46.290 < 2e-16 ***
ORIGIN_SZ534 2.5321314 0.0492006 51.465 < 2e-16 ***
ORIGIN_SZ536 0.5091388 0.0648876 7.846 4.28e-15 ***
ORIGIN_SZ537 -1.0663925 0.1655347 -6.442 1.18e-10 ***
ORIGIN_SZ538 -1.6661192 0.2146829 -7.761 8.44e-15 ***
ORIGIN_SZ551 -0.3023224 0.0961191 -3.145 0.001659 **
ORIGIN_SZ552 0.1011391 0.0725397 1.394 0.163239
ORIGIN_SZ553 -0.5301834 0.0560522 -9.459 < 2e-16 ***
ORIGIN_SZ554 1.7944560 0.0492664 36.424 < 2e-16 ***
ORIGIN_SZ555 1.4901238 0.0517085 28.818 < 2e-16 ***
ORIGIN_SZ559 0.4692962 0.0912409 5.143 2.70e-07 ***
ORIGIN_SZ560 0.2739061 0.1038874 2.637 0.008375 **
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ORIGIN_SZ573 0.5436282 0.0689056 7.889 3.03e-15 ***
ORIGIN_SZ574 1.1232763 0.0966696 11.620 < 2e-16 ***
ORIGIN_SZ575 3.9411964 0.0487294 80.879 < 2e-16 ***
ORIGIN_SZ576 1.6960043 0.0496220 34.178 < 2e-16 ***
ORIGIN_SZ578 -2.6066088 0.2098795 -12.420 < 2e-16 ***
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ORIGIN_SZ583 0.1824415 0.1350395 1.351 0.176688
ORIGIN_SZ584 1.2821039 0.0888263 14.434 < 2e-16 ***
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ORIGIN_SZ594 0.2442080 0.0688866 3.545 0.000393 ***
ORIGIN_SZ595 0.0314801 0.0538899 0.584 0.559115
ORIGIN_SZ596 1.3667225 0.0494371 27.646 < 2e-16 ***
ORIGIN_SZ597 -1.0456896 0.1083244 -9.653 < 2e-16 ***
ORIGIN_SZ603 -0.3628031 0.1457189 -2.490 0.012783 *
ORIGIN_SZ604 -0.2374258 0.1509075 -1.573 0.115645
ORIGIN_SZ615 -0.8622917 0.0878927 -9.811 < 2e-16 ***
ORIGIN_SZ616 -0.0845604 0.0615341 -1.374 0.169378
ORIGIN_SZ617 -1.0055094 0.0609173 -16.506 < 2e-16 ***
ORIGIN_SZ618 2.2284970 0.0491337 45.356 < 2e-16 ***
ORIGIN_SZ620 -1.2589433 0.0914458 -13.767 < 2e-16 ***
ORIGIN_SZ637 -0.6513854 0.0659606 -9.875 < 2e-16 ***
ORIGIN_SZ638 2.0140469 0.0491342 40.991 < 2e-16 ***
ORIGIN_SZ657 0.8395428 0.0561541 14.951 < 2e-16 ***
ORIGIN_SZ658 1.1203605 0.0507558 22.074 < 2e-16 ***
ORIGIN_SZ659 1.3967167 0.0497614 28.068 < 2e-16 ***
ORIGIN_SZ66 0.0157813 0.2412587 0.065 0.947846
ORIGIN_SZ660 2.8765822 0.0488717 58.860 < 2e-16 ***
ORIGIN_SZ662 3.0645940 0.0499459 61.358 < 2e-16 ***
ORIGIN_SZ67 0.9609667 0.0699158 13.745 < 2e-16 ***
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ORIGIN_SZ679 2.5500343 0.0490762 51.961 < 2e-16 ***
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ORIGIN_SZ680 2.5769680 0.0490069 52.584 < 2e-16 ***
ORIGIN_SZ681 0.8865212 0.0523916 16.921 < 2e-16 ***
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ORIGIN_SZ701 1.0915099 0.0505557 21.590 < 2e-16 ***
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ORIGIN_SZ730 -0.0655610 0.1020486 -0.642 0.520582
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ORIGIN_SZ787 1.5450001 0.0508883 30.361 < 2e-16 ***
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ORIGIN_SZ805 2.6694113 0.0489052 54.583 < 2e-16 ***
ORIGIN_SZ806 1.7028675 0.0493265 34.522 < 2e-16 ***
ORIGIN_SZ807 2.4495610 0.0493843 49.602 < 2e-16 ***
ORIGIN_SZ808 0.5260196 0.0554078 9.494 < 2e-16 ***
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ORIGIN_SZ810 1.5641298 0.0498934 31.349 < 2e-16 ***
ORIGIN_SZ814 0.9421254 0.0612773 15.375 < 2e-16 ***
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ORIGIN_SZ830 1.6192722 0.0499945 32.389 < 2e-16 ***
ORIGIN_SZ831 3.4589025 0.0487213 70.994 < 2e-16 ***
ORIGIN_SZ832 2.8071430 0.0492101 57.044 < 2e-16 ***
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ORIGIN_SZ844 -0.7864059 0.1024602 -7.675 1.65e-14 ***
ORIGIN_SZ846 1.6861912 0.0496438 33.966 < 2e-16 ***
ORIGIN_SZ847 1.6537378 0.0495766 33.357 < 2e-16 ***
ORIGIN_SZ848 1.4951970 0.0494963 30.208 < 2e-16 ***
ORIGIN_SZ849 0.5823333 0.0509558 11.428 < 2e-16 ***
ORIGIN_SZ850 1.9355393 0.0493246 39.241 < 2e-16 ***
ORIGIN_SZ851 2.0113029 0.0491331 40.936 < 2e-16 ***
ORIGIN_SZ852 1.4651061 0.0498570 29.386 < 2e-16 ***
ORIGIN_SZ853 3.2895141 0.0492655 66.771 < 2e-16 ***
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ORIGIN_SZ855 -0.9065940 0.0971171 -9.335 < 2e-16 ***
ORIGIN_SZ856 1.1543453 0.0587598 19.645 < 2e-16 ***
ORIGIN_SZ86 -0.9868308 0.0973280 -10.139 < 2e-16 ***
ORIGIN_SZ866 1.0066866 0.0571806 17.605 < 2e-16 ***
ORIGIN_SZ867 0.7533821 0.0518525 14.529 < 2e-16 ***
ORIGIN_SZ868 0.8638732 0.0514383 16.794 < 2e-16 ***
ORIGIN_SZ869 2.0331093 0.0503843 40.352 < 2e-16 ***
ORIGIN_SZ87 1.5002095 0.1318262 11.380 < 2e-16 ***
ORIGIN_SZ870 2.8930829 0.0488090 59.274 < 2e-16 ***
ORIGIN_SZ871 2.7667302 0.0493668 56.044 < 2e-16 ***
ORIGIN_SZ872 0.1349613 0.0531888 2.537 0.011168 *
ORIGIN_SZ873 0.5355640 0.0516619 10.367 < 2e-16 ***
ORIGIN_SZ874 0.3917353 0.0518701 7.552 4.28e-14 ***
ORIGIN_SZ875 -0.5954092 0.1090877 -5.458 4.81e-08 ***
ORIGIN_SZ876 -1.4033120 0.0955576 -14.686 < 2e-16 ***
ORIGIN_SZ877 1.0263154 0.0568459 18.054 < 2e-16 ***
ORIGIN_SZ88 2.0821410 0.0591353 35.210 < 2e-16 ***
ORIGIN_SZ887 0.4043641 0.0538946 7.503 6.24e-14 ***
ORIGIN_SZ888 0.9275887 0.0509022 18.223 < 2e-16 ***
ORIGIN_SZ889 -1.2034270 0.0722183 -16.664 < 2e-16 ***
ORIGIN_SZ89 -0.1918784 0.1884608 -1.018 0.308614
ORIGIN_SZ890 2.2041581 0.0490861 44.904 < 2e-16 ***
ORIGIN_SZ891 0.7949040 0.0533588 14.897 < 2e-16 ***
ORIGIN_SZ893 2.1604888 0.0490189 44.075 < 2e-16 ***
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ORIGIN_SZ895 0.2839041 0.0559232 5.077 3.84e-07 ***
ORIGIN_SZ896 -1.0557229 0.0778987 -13.553 < 2e-16 ***
ORIGIN_SZ897 -1.5919544 0.0830914 -19.159 < 2e-16 ***
ORIGIN_SZ898 0.3561963 0.0636401 5.597 2.18e-08 ***
ORIGIN_SZ90 0.7284854 0.1126265 6.468 9.92e-11 ***
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DESTIN_SZ991 1.8631298 0.0555653 33.530 < 2e-16 ***
DESTIN_SZ992 2.0208901 0.0548401 36.851 < 2e-16 ***
DESTIN_SZ993 1.0246326 0.0558684 18.340 < 2e-16 ***
DESTIN_SZ994 1.2994702 0.0558729 23.258 < 2e-16 ***
DESTIN_SZ995 2.0152883 0.0547814 36.788 < 2e-16 ***
DESTIN_SZ996 1.2728739 0.0564216 22.560 < 2e-16 ***
DESTIN_SZ997 0.3874822 0.0677213 5.722 1.05e-08 ***
DESTIN_SZ998 2.7083900 0.0541109 50.053 < 2e-16 ***
DESTIN_SZ999 2.0389976 0.0548053 37.204 < 2e-16 ***
log(DIST) -1.5622080 0.0004961 -3148.680 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 27137198 on 61827 degrees of freedom
Residual deviance: 5675541 on 60186 degrees of freedom
AIC: 5968031
Number of Fisher Scoring iterations: 10CalcRSquared(dbcSIM_Poisson$data$TRIPS,
dbcSIM_Poisson$fitted.values)[1] 0.6682232Conclusion of Doubly_Constrained model
Doubly_Constrained model demonstrates significant statistical strength, with all P-values being less than the 0.05 threshold, indicating a significant positive effect of the variables in the model on the predicted outcomes. The R-squared value of the model is 66.8%, suggesting that it accounts for a substantial portion of the variability in the response variable, indicating a good fit. Additionally, the model required 10 iterations of Fisher Scoring to converge, showing that the model underwent a reasonable number of iterations before reaching the optimal solution. Overall, the performance of this doubly constrained model is quite satisfactory. It effectively captures key features of the data, providing reliable predictions of the response variable. However, given that there is still room for improvement in the residual deviance, further exploration of additional explanatory variables or model adjustments might be needed to optimize performance and enhance explanatory power.
model_list <- list(
Origin_Constrained = orcSIM_Poisson,
Doubly_Constrained = dbcSIM_Poisson)compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
------------------------------------
Origin_Constrained | glm | 392.509
Doubly_Constrained | glm | 303.003Modle Camparation Conclusion
The smaller the RMSE value, the smaller the error of the model. From the results, it can be seen that the Doubly Constrained Model (glm) has a smaller error compared to the Origin Constrained Model (glm). Consequently, in terms of performance, the Doubly Constrained Model (glm) is superior to the Origin Constrained Model (glm).
6,Visualization.
df <- as.data.frame(orcSIM_Poisson$fitted.values) %>%
round(digits = 0)inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM_Poisson$fitted.values")df <- as.data.frame(dbcSIM_Poisson$fitted.values) %>%
round(digits = 0)inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(dbcTRIPS1 = "dbcSIM_Poisson$fitted.values")orc_p <- ggplot(data = inter_zonal_flow,
aes(x = orcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,150000),
ylim=c(0,150000))
dbc_p <- ggplot(data = inter_zonal_flow,
aes(x = dbcTRIPS1,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,150000),
ylim=c(0,150000))ggarrange(orc_p, dbc_p,
ncol = 2,
nrow = 1)`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
Conclusion of Visualization
The chart indicates that the Doubly_Constrained Model has a better fit than the Origin_Constrained Model, as evidenced by the smaller dispersion of points around the trend line, which suggests a lower error in the Doubly_Constrained Model compared to the Origin_Constrained Model.
7,Limitations
Limitations: 1，We have only compared two models; ideally, we could compare a wider range of models to select the most optimal one. 2，The data used were selectively chosen, which introduces the possibility of subjective bias in the dataset. 3，The model could benefit from a stepwise evaluation to determine if reducing the number of variables might increase the fit. 4，Due to memory limitations, ‘mapview’ cannot be used and the image lacks boundaries.